In the field of signal processing, the signals of interest can be represented sparsely by using few coefficients in an appropriately selected orthonormal basis. Exemplarily, the Fourier basis is used for band limited signals or wavelet bases for piecewise continuous signals, such as images. While a small number of coefficients in the respective bases are enough to represent such signals, the Nyquist/Shannon sampling theorem suggests a sampling rate that is at least twice the signal bandwidth. Such a sampling rate is known in the art as the Nyquist rate. In many cases, the indicated sampling rate is much higher than the sufficient number of coefficients.
Recently, the Compressed Sensing (CS) framework was introduced aiming at sampling the signals not according to their bandwidth, but rather in accordance with their information content, that is, the number of degrees of freedom of the signal. This paradigm for sampling suggests a lower sampling rate compared to the classical sampling theory for signals that have sparse representation in some given basis. Typical signals that arise naturally in astronomy and biomedical imaging fit this model.